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Physics for Scientists and Enginee...

10th Edition
Raymond A. Serway + 1 other
Publisher: Cengage Learning
ISBN: 9781337553278

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BuyFindarrow_forward

Physics for Scientists and Enginee...

10th Edition
Raymond A. Serway + 1 other
Publisher: Cengage Learning
ISBN: 9781337553278
Chapter 1, Problem 10P
Textbook Problem
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(a) Assume the equation x = At3 + Bt describes the motion of a particular object, with x having the dimension of length and t having the dimension of time. Determine the dimensions of the constants A and B. (b) Determine the dimensions of the derivative dx/dt = 3At2 + B.

(a)

To determine

The dimensions of the constant A and B in the equation x=At3+Bt.

Explanation of Solution

Write the equation of the motion of a particular object having x as function of t

    x=At3+Bt                                                  (I)

Here, x is the position of the object, t is the time, A is any constant and B is any constant.

The dimension of x is L and the dimension of t is T.

Assume the dimension of A is LaTb and the dimension of B is LcTd.

Since the given equation is dimensionally correct. So, the dimension on left side must balance the dimension of right side.

Equating the dimension of x and At3.

Substitute L for x and LaTb for At3.

    L=(LaTb)T3L=LaTb+3

Equating the exponent on both side of the equation,

    a=1

  b+3=0b=3

Substitute 1 for a and 3 for b to find the dimension of A

(b)

To determine

The dimensions of the derivative dxdt in the equation dxdt=3At2+B.

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Physics for Scientists and Engineers
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